Q. An electron and a proton enter region of uniform magnetic field in a direction at right angles to the field with the same kinetic energy. They describe circular paths of radius $r_{e}$ and $r_{p}$ respectively. Then
A) $r_{e} = r_{P}$
B) $r_{e} < r_{P}$
C) $r_{e} > r_{P}$
D) $r_{e}$ may be less than or greater than $r_{P}$ depending on the direction of the magnetic field
Explanation
(b) $r = \frac{\sqrt{2mK}}{qB}i.e.\ \ r \propto \frac{\sqrt{m}}{q}$
Here kinetic energy $K$ and $B$ are same
$\therefore\frac{r_{e}}{r_{p}} = \sqrt{\frac{m_{e}}{m_{p}}} \times \frac{q_{p}}{q_{e}} \Rightarrow \frac{r_{e}}{r_{p}} = \sqrt{\frac{m_{e}}{m_{p}}}\ \left\lbrack \because q_{e} = q_{p} \right\rbrack$
Since $m_{e} < m_{p},$ therefore $r_{e} < r_{p}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.